Britain will not hold a referendum on the final deal to leave the European Union or seek to delay its exit date, Prime Minister Theresa May said on Monday, after two ministerial resignations put her Brexit plan at risk.

May said that Britain would not look to extend Article 50, the notice of intention to leave the EU, and that British people wanted the government to deliver Brexit rather than voting again on the deal.

Britain is due to leave the EU on March 29, 2019, but May's bid to finalise a strategy was rocked on Monday by the resignations of Foreign Secretary Boris Johnson and Brexit minister David Davis in protest at her plan for Brexit.

Asked about a possible leadership challenge given the splits in her government, May smiled and said: "nice try, but I'm getting on with the job of delivering what the British people want."